Computation, Physics and Beyond: International Workshop on Theoretical Computer Science, WTCS 2012, Dedicated to Cristian S. Calude on the Occasion of His 60th Birthday, Auckland, New Zealand, February 21-24, 2012, Revised Selected and Invited Papers

438 Pages·2012·3.263 MB·English

by  Solomon Marcus (auth.), Michael J. Dinneen, Bakhadyr Khoussainov, André Nies (eds.)

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Michael J. Dinneen Bakhadyr Khoussainov
André Nies (Eds.)
Computation, Physics
and Beyond
International Workshop
on Theoretical Computer Science, WTCS 2012
Dedicated to Cristian S. Calude
on the Occasion of His 60th Birthday
Auckland, New Zealand, February 21-24, 2012
Revised Selected and Invited Papers
1 3
VolumeEditors
MichaelJ.Dinneen
BakhadyrKhoussainov
AndréNies
UniversityofAuckland
DepartmentofComputerScience
PrivateBag92019,Auckland1142,NewZealand
E-mail:{mjd,bmk,andre}@cs.auckland.ac.nz
ISSN0302-9743 e-ISSN1611-3349
ISBN978-3-642-27653-8 e-ISBN978-3-642-27654-5
DOI10.1007/978-3-642-27654-5
SpringerHeidelbergDordrechtLondonNewYork
LibraryofCongressControlNumber:2011944976
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Preface
The International Workshop on Theoretical Computer Science (WTCS 2012),
dedicated to Cristian Calude’s 60thbirthday,took place during February21–24
in2012inAuckland,NewZealand.ThisvolumetitledComputation,Physics and
Beyond, based on WTCS 2012, is published in the LNCS Festschrifts Series by
Springer. The volume contains contributions from invited speakers and regular
papers that present either expository/survey results or original research in the
following areas (in which Cristian Calude has either made significant contribu-
tions or has an interest):
– Algorithmic information theory
– Algorithms
– Automata and formal languages
– Computing and natural sciences
– Computability and applications
– Logic and applications
– Philosophy of computation
– Physics and computation
– Unconventional models of
computation
Prof. Cristian (Cris) S. Calude
The followingeminentresearcherswereinvitedtogivelectures atthe confer-
ence and contribute to the Festschrift volume.
D. Bridges (Canterbury University) B. Pavlov (Massey University)
C. Cˆampeanu (University of Prince G. Rozenberg (Leiden University)
Edward Island) A. Shen (University of Marseille)
B. Cooper (Leeds University) L. Staiger (Martin Luther University)
R. Freivalds (University of Latvia) K. Svozil (Vienna Technical University)
H. Ju¨rgensen (University of Western K. Tadaki (Chuo University, Tokyo)
Ontario) S. Yu (University of Western Ontario)
G. Longo (E´cole Polytechnique, Paris) L. Vˆı¸t˘a (NZ Customs)
S. Marcus (Romanian Academy) H. Zenil (Wolfram Research)
H.Maurer(GrazTechnicalUniversity) M. Zimand (Towson Univ)
J. Patarin (Universit´e Versailles) S. Wolfram (Wolfram Research)
VI Preface
Other invited contributors agreeing to contribute to this Festschrift volume
dedicated to Cris include:
G. Chaitin (IBM Research, New York) Gh. Pa˘un (Romanian Academy)
R. Downey (Victoria University, NZ) A. Salomaa (Turku University)
M. Dumitrescu (University of Bucharest) K. Salomaa (Kingston University)
L. Kari (University of Western Ontario) I. Streinu (Smith College)
Y. Manin (Max Planck Institute) I. Tomescu (University of Bucharest)
The Program Committee consisted of B. Cooper, F. Costa, M. J. Dinneen,
P.Hertling,B.Khoussainov(Chair),F.Kroon,Y.Matiyasevich,A.Nies,Gh.P˘aun,
G.Rozenberg,K.Salomaa,L.Staiger,A.Shen,F.StephanandM.Zimand.They
appreciate the additional work done by the following referees for the conference
volume:
Vasco Brattka Rupert H¨olzl Ulrich Speidel
Elena Calude Yun-Bum Kim Mike Stay
Rodney Downey Gaven Martin Kohtaro Tadaki
Noam Greenberg Erik Palmgren Karl Svozil
The careers of the three editors of this book have been influenced by Cris’
research in algorithmic randomness, as well as his tireless administrating and
organizing work. Soon after his arrival in Auckland in the early 1990s, Cris,
jointlywith DouglasBridges,whowasthen atthe UniversityofWaikato,estab-
lished the Centre for Discrete Mathematics and Theoretical Computer Science
(CDMTCS).Thisledtotheformationofthefirstcomputersciencetheorygroup
inNew Zealand.With the creationofthe CDMTCS andhis researchwork,Cris
put the Computer Science Department at the University of Auckland on the
map.Allthreeofuswererecruitedbythe departmentwithstrongsupportfrom
Cris. In the mid-1990s, Calude, jointly with Khoussainov, Hertling and Wang,
wroteafewpapers,including“RecursivelyenumerablerealsandChaitinOmega
numbers,” which was published in the Proceedings of STACS 1998, and later in
the journal Theoretical Computer Science. These papers, along with early work
by Chaitin, Kuˇcera,Kurtz, Solovayand Terwijn, laidthe foundationfor the de-
velopment of the modern theory of algorithmic randomness as expressed in the
work of Downey, Hirschfeldt, Miller, Nies, Slaman, Stephan, and many others.
The paper by Calude, Khoussainov, Hertling and Wang for the first time
studied the concept of Solovay reducibility (from a 1975 manuscript) on the
realnumbersandintroducedcomputablyenumerablepresentationsofreals.The
authorsestablishedsomefundamentalpropertiesofSolovayreducibility,suchas
the equivalence classes of computably enumerable reals form an upper semi-
lattice. The (Chaitin) Ω numbers form an equivalence class which is the largest
element in this semi-lattice. This paper proposed the problem of whether every
random computably enumerable real is a Ω number, i.e., corresponds to the
largestelementinthesemi-lattice.Thisproblemattractedtheattentionofmany
experts in the theory of randomness and computability. Kuˇcera and Slaman
Preface VII
answered the question positively in “Randomness and recursive enumerability”
(SIAM J. of Computing) in 2001.
A related 2002 paper also inspired by the work of Cris and his collaborators
is “Randomness, computability and density” by Downey, Hirschfeldt and Nies
(SIAM J. of Computing), where the density of the semilattice is established. A
furtherquestionwaswhetherforeverysplittingofanΩ numberasasumoftwo
computably enumerable reals, one of the two has to be an Ω number as well.
Theyansweredthequestionintheaffirmative.(Curiously,lateronitturnedout
that O. Demuth, a constructivist working in isolation in Prague, already had
known this in 1975.)
Cris’ work was essential for establishing the leading role of New Zealand in
theareaofalgorithmicrandomness,whichisevidencedbytherecentpublication
of Nies’ book Computability and Randomness published by Oxford University
Press in 2009,and Downey and (former Wellington postdoc) Hirschfeldt’s book
Algorithmic Randomness and Complexity by Springer in 2010.
An Ω number is simultaneously computably enumerable and random; its
weak form of computable approximability (the first property) is limited by the
last property which implies bi-immunity, i.e., every algorithm can compute at
most finitely many exact bits of such a number (none in the case of a Solovay’s
number, a special type of Ω number). The work Michael Dinneen did with Cris
and,initially,withtheirformerPhDstudentC.-K.Shu,combinedthetheoretical
analysiswithanextensivecomputationtocalculateexactlythevaluesoffinitely
many initial bits of a natural Ω number (64 in the first case). This result—
the first computation of “a glimpse of randomness”—was extensively cited and
commented on (for example, in the New Scientist); its meaning is discussed in
Chaitin’s paper included in this volume. This work paved the way for a more
practicalandcomplexity-theoreticapproachtorandomness,whichincludestheo-
reticalandexperimentalstudiesofquantumrandomness(workjointlydonewith
Cris, M. Dumitrescu and K. Svozil). Michael appreciates his cooperation with
Cris in the emerging field of unconventional/natural computing, e.g., the bead
search/sortingwas developed with their former PhD student J. Arulanandham,
and in the study of the complexity of mathematical problems (joint work with
E.Calude).They organizedmanyCDMTCS internationalconferencestogether,
including most editions in the series of conferences “Unconventional Computa-
tion” that started in Auckland in 1998.
We all value our friendship with Cris and the mentoring advice he has pro-
vided over the past 16 years. Our close relationship with Cris goes beyond aca-
demic collaboration.For instance, Bakh wishes that he could play tennis at the
levelofCris;MichaelisenviousofCris’airguncollection;Andr´ewisheshecould
also organize a workshop on a boat going down the Nile river.
The local Organizing Committee at the University of Auckland wishes to
acknowledgethecontributionsofGillDobbieandBobDoran.WethanktheDe-
partment of Computer Science (University of Auckland), the Faculty of Science
(University of Auckland), and the New Zealand Marsden Fund for monetary
support. Last but not least, it is a great pleasure to thank the fine co-operation
VIII Preface
withtheLectureNotes in Computer Science teamofSpringerforproducingthis
volume in time for the conference.
This book is organized as follows into themes related to Cris’ research area.
The first part consists of a couple of papers discussing Cris’ life achievements.
This is then followed by papers in the three general areas of complexity, com-
putability and randomness; physics, philosophy (and logic) and computation;
and algorithms, automata and formal models (including unconventional com-
puting). Finally, we mention that the front cover art of this book highlights the
first40exactbitsofanΩ numberrecentlycomputedbyCrisandthefirsteditor.
November 2011 Michael J. Dinneen
Bakhadyr Khoussainov
Andr´e Nies
Table of Contents
Life Story
The Art of Reaching the Age of Sixty .............................. 1
Solomon Marcus
Calude as Father of One of the Computer Science Journals............ 20
Hermann Maurer
Complexity, Computability and Randomness
Random Semicomputable Reals Revisited ........................... 31
Laurent Bienvenu and Alexander Shen
Constructing the Infimum of Two Projections ....................... 46
Douglas S. Bridges and Luminita S. Vˆı¸t˘a
Bounded Randomness ............................................ 59
Paul Brodhead, Rod Downey, and Keng Meng Ng
A Note on Blum Static Complexity Measures........................ 71
Cezar Caˆmpeanu
A Program-Size Complexity Measure for Mathematical Problems and
Conjectures ..................................................... 81
Michael J. Dinneen
On Degrees of Randomness and Genetic Randomness................. 94
Monica Dumitrescu
Hartmanis-Stearns Conjecture on Real Time and Transcendence ....... 105
Ru¯sin¸ˇs Freivalds
Learning Families of Closed Sets in Matroids ........................ 120
Ziyuan Gao, Frank Stephan, Guohua Wu, and Akihiro Yamamoto
Invariance and Universality of Complexity .......................... 140
Helmut Ju¨rgensen
Demuth’s Path to Randomness .................................... 159
Anton´ın Kuˇcera and Andr´e Nies
A Computability Challenge: Asymptotic Bounds for Error-Correcting
Codes .......................................................... 174
Yuri I. Manin